Over and over, I saw students who really committed to their teams get great benefits out of it. Now, I think pure mathematical research is a crucial investment in the future of our society. I have just one item to add to your lists: And, while skilled instructors with an excellent command of the mathematical field may be more common than skilled researchers, they are going to be rare as well. I very much doubt you can visually perceive the difference between a straight line and two lines making an angle of with each other and this can make a substantial difference in an integral. He should do poorly on the exam — a C minus or a D. Organization I was assigned two sections of 32 students each, which dwindled to 30 each over the course of the term.
I have just one item to add to your lists: Partly, I think this is important for maintaining student motivation. I would be happier if the exams had one or two more basic questions, with the rest staying as they are. The athletes really got a kick out of table 1 from this paper , showing how world class runners accelerate second by second; a lot of students enjoyed figuring out how long a runway a Ford Mustang needs to accelerate to mph using the data here. The mathlab is like a live-action version of math. Organization I was assigned two sections of 32 students each, which dwindled to 30 each over the course of the term. I am curious — the median score on the Putnam exam is a zero.
However, when I did force them to, mat often got a lot out of it. The course coordinators really stressed how much the course focused on groupwork. My intended audience here is others who are about to teach Calculus at Michigan, or people who are wondering what it would be like to set up a Michigan-style program in their own departments.
There are plenty of people who love math so much that they will continually learn and study new mathematics.
Some thoughts on teaching Michigan calculus | Secret Blogging Seminar
For example, when counting boxes under a curve, they pointed at the squares in a random order, rather than sweeping from left to right, top to bottom. At public schools in times of budget cutbacks, taxpayers ought to feel that in funding a math department they are not simply subsidizing an academic lifestyle that has nothing to do with them. I enjoyed the real world examples. Every department has three distinct curricula: What was difficult about this was that it made grading very difficult to predict.
I had two students who, when I asked them for teammate preferences, specifically asked not to be put with students in the top half of the class.
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Calculus at Michigan focuses very heavily on working with data and on understanding what computation to do, rather than how to do it. But I hope that many politicians would see the point.
I want to take the opportunity to brag about the most fun example of this: It builds personal connections within a department. However, I can list some positive things which I brought to my teaching that come from my background. This paradox demonstrates the point very vividly. For example, one question asked students to numerically approximate at.
SE and, while the questions are less exciting, the challenge of being hoework to face with the questioner makes up for it. When I teach this class again, I will make a similar deal.
Before answering, I want to point out that university departments are not idealized firms, who aim to produce a service as efficiently as possible.
In each case, for many of my classmates, that was the beginning of the end.
Some thoughts on teaching Michigan calculus
After all, you homewirk the department significantly more than a graduate student! I would be happier if the exams had one or two more basic questions, with the rest staying as they are.
I talked about how the error rate in a left hand or right hand Riemann sum is controlled by the steepness of the function, while the error in the average is controlled by the curvy-ness. I have just one item to add to your lists: But I think a lot of it comes from continuously thinking about a wide range of mathematics over the last twelve years.
Over and over, I homewodk students who really committed to their teams get great benefits out of it. The exams, especially the last two, were almost all challenging conceptual problems.
Moreover, while the course coordinators are highly experienced professionals, almost all of the day-to-day instruction is done by a small army of grad students and postdocs; I was one of the very few tenured or tenure track people teaching calculus this term. I had a lot of fun going to the mathlab.
Organization I was assigned two sections of 32 students each, which dwindled to 30 each over the course of the term.